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Solution
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Q.1 Correct
Q.1 In-correct
Q.1 Unattempt

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet.

In the light of the above statements, choose the correct answer from the options given below :



JEE Main 2025 (Online) 22nd January Evening Shift

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.

Reason (R) : The mass of the pendulum remains unchanged at Earth and the other planet.

In the light of the above statements, choose the correct answer from the options given below :



JEE Main 2025 (Online) 22nd January Evening Shift
Q.2 Correct
Q.2 In-correct
Q.2 Unattempt

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of $y$ is(Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$ )



JEE Main 2025 (Online) 23rd January Morning Shift

A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is $y \pi \times 10^{-2} \mathrm{~s}$, where the value of $y$ is(Acceleration due to gravity, $g=10 \mathrm{~m} / \mathrm{s}^2$, density of water $=10^3 \mathrm{~kg} / \mathrm{m}^3$ )



JEE Main 2025 (Online) 23rd January Morning Shift
Q.3 Correct
Q.3 In-correct
Q.3 Unattempt
A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then $\frac{\mathrm{D}}{\mathrm{d}}$ is

JEE Main 2025 (Online) 24th January Morning Shift
A particle is executing simple harmonic motion with time period 2 s and amplitude 1 cm . If D and d are the total distance and displacement covered by the particle in 12.5 s , then $\frac{\mathrm{D}}{\mathrm{d}}$ is

JEE Main 2025 (Online) 24th January Morning Shift
Q.4 Correct
Q.4 In-correct
Q.4 Unattempt

A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1 \mathrm{~m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph



JEE Main 2025 (Online) 24th January Evening Shift

A particle oscillates along the $x$-axis according to the law, $x(\mathrm{t})=x_0 \sin ^2\left(\frac{\mathrm{t}}{2}\right)$ where $x_0=1 \mathrm{~m}$. The kinetic energy $(\mathrm{K})$ of the particle as a function of $x$ is correctly represented by the graph



JEE Main 2025 (Online) 24th January Evening Shift
Q.5 Correct
Q.5 In-correct
Q.5 Unattempt

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Knowing initial position $\mathrm{x}_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.

Reason (R) : The amplitude and phase can be expressed in terms of $\mathrm{X}_0$ an $\mathrm{p}_0$.

In the light of the above statements, choose the correct answer from the options given below :



JEE Main 2025 (Online) 28th January Evening Shift

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Knowing initial position $\mathrm{x}_0$ and initial momentum $p_0$ is enough to determine the position and momentum at any time $t$ for a simple harmonic motion with a given angular frequency $\omega$.

Reason (R) : The amplitude and phase can be expressed in terms of $\mathrm{X}_0$ an $\mathrm{p}_0$.

In the light of the above statements, choose the correct answer from the options given below :



JEE Main 2025 (Online) 28th January Evening Shift
Q.6 Correct
Q.6 In-correct
Q.6 Unattempt

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.

Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.

In the light of the above statements, choose the most appropriate answer from the options given below :



JEE Main 2025 (Online) 29th January Morning Shift

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.

Reason (R) : Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa.

In the light of the above statements, choose the most appropriate answer from the options given below :



JEE Main 2025 (Online) 29th January Morning Shift
Q.7 Correct
Q.7 In-correct
Q.7 Unattempt

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is



JEE Main 2025 (Online) 29th January Evening Shift

Two bodies A and B of equal mass are suspended from two massless springs of spring constant k1 and k2, respectively. If the bodies oscillate vertically such that their amplitudes are equal, the ratio of the maximum velocity of A to the maximum velocity of B is



JEE Main 2025 (Online) 29th January Evening Shift
Q.8 Correct
Q.8 In-correct
Q.8 Unattempt

A particle is subjected to two simple harmonic motions as :$$x_1=\sqrt{7} \sin 5 \mathrm{tcm}$$and $x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}$where $x$ is displacement and $t$ is time in seconds.The maximum acceleration of the particle is $x \times 10^{-2} \mathrm{~ms}^{-2}$. The value of $x$ is :



JEE Main 2025 (Online) 2nd April Morning Shift

A particle is subjected to two simple harmonic motions as :$$x_1=\sqrt{7} \sin 5 \mathrm{tcm}$$and $x_2=2 \sqrt{7} \sin \left(5 t+\frac{\pi}{3}\right) \mathrm{cm}$where $x$ is displacement and $t$ is time in seconds.The maximum acceleration of the particle is $x \times 10^{-2} \mathrm{~ms}^{-2}$. The value of $x$ is :



JEE Main 2025 (Online) 2nd April Morning Shift
Q.9 Correct
Q.9 In-correct
Q.9 Unattempt
JEE Main 2025 (Online) 3rd April Morning Shift Physics - Simple Harmonic Motion Question 2 English

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 3rd April Morning Shift
JEE Main 2025 (Online) 3rd April Morning Shift Physics - Simple Harmonic Motion Question 2 English

Two blocks of masses $m$ and $M,(M>m)$, are placed on a frictionless table as shown in figure. A massless spring with spring constant k is attached with the lower block. If the system is slightly displaced and released, then ( $\mu=$ coefficient of friction between the two blocks)

A. The time period of small oscillation of the two blocks is $T=2 \pi \sqrt{\frac{(m+M)}{k}}$

B. The acceleration of the blocks is $a=-\frac{k x}{M+m}$ ( $x=$ displacement of the blocks from the mean position)

C. The magnitude of the frictional force on the upper block is $\frac{m \mu|x|}{M+m}$

D. The maximum amplitude of the upper block, if it does not slip, is $\frac{\mu(M+m) g}{k}$

E. Maximum frictional force can be $\mu(\mathrm{M}+\mathrm{m}) \mathrm{g}$.

Choose the correct answer from the options given below :



JEE Main 2025 (Online) 3rd April Morning Shift
Q.10 Correct
Q.10 In-correct
Q.10 Unattempt

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?



JEE Main 2025 (Online) 4th April Morning Shift

Two simple pendulums having lengths $l_1$ and $l_2$ with negligible string mass undergo angular displacements $\theta_1$ and $\theta_2$, from their mean positions, respectively. If the angular accelerations of both pendulums are same, then which expression is correct?



JEE Main 2025 (Online) 4th April Morning Shift
Q.11 Correct
Q.11 In-correct
Q.11 Unattempt

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be



JEE Main 2025 (Online) 8th April Evening Shift

A block of mass 2 kg is attached to one end of a massless spring whose other end is fixed at a wall. The spring-mass system moves on a frictionless horizontal table. The spring's natural length is 2 m and spring constant is 200 N/m. The block is pushed such that the length of the spring becomes 1 m and then released. At distance x m (x < 2) from the wall, the speed of the block will be



JEE Main 2025 (Online) 8th April Evening Shift
Q.12 Correct
Q.12 In-correct
Q.12 Unattempt

A particle executes simple harmonic motion with an amplitude of 4cm. At the mean position, velocity of the particle is 10cm∕ s. The distance of the particle from the mean position when its speed becomes 5cm∕ s is √α cm, where α = ___

[27-Jan-2024 Shift 1]

A particle executes simple harmonic motion with an amplitude of 4cm. At the mean position, velocity of the particle is 10cm∕ s. The distance of the particle from the mean position when its speed becomes 5cm∕ s is √α cm, where α = ___

[27-Jan-2024 Shift 1]
Q.13 Correct
Q.13 In-correct
Q.13 Unattempt

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle (θ) of thread deflection in the extreme position will be :

[27-Jan-2024 Shift 2]

A ball suspended by a thread swings in a vertical plane so that its magnitude of acceleration in the extreme position and lowest position are equal. The angle (θ) of thread deflection in the extreme position will be :

[27-Jan-2024 Shift 2]
Q.14 Correct
Q.14 In-correct
Q.14 Unattempt

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x/8, where x =____

[29-Jan-2024 Shift 1]

When the displacement of a simple harmonic oscillator is one third of its amplitude, the ratio of total energy to the kinetic energy is x/8, where x =____

[29-Jan-2024 Shift 1]
Q.15 Correct
Q.15 In-correct
Q.15 Unattempt

A simple harmonic oscillator has an amplitude A and time period 6π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = √3/2 A will be π/x s, where x = _____:

[29-Jan-2024 Shift 2]

A simple harmonic oscillator has an amplitude A and time period 6π second. Assuming the oscillation starts from its mean position, the time required by it to travel from x = A to x = √3/2 A will be π/x s, where x = _____:

[29-Jan-2024 Shift 2]
Q.16 Correct
Q.16 In-correct
Q.16 Unattempt

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be _____s. [. take g = π2 ms−2]

[30-Jan-2024 Shift 2]

A simple pendulum is placed at a place where its distance from the earth's surface is equal to the radius of the earth. If the length of the string is 4m, then the time period of small oscillations will be _____s. [. take g = π2 ms−2]

[30-Jan-2024 Shift 2]
Q.17 Correct
Q.17 In-correct
Q.17 Unattempt

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A/3. The new amplitude of motion is nA/3. The value of n is___

[31-Jan-2024 Shift 1]

A particle performs simple harmonic motion with amplitude A. Its speed is increased to three times at an instant when its displacement is 2A/3. The new amplitude of motion is nA/3. The value of n is___

[31-Jan-2024 Shift 1]
Q.18 Correct
Q.18 In-correct
Q.18 Unattempt

The time period of simple harmonic motion of mass M in the given figure is π  where the value of α is _____

[31-Jan-2024 Shift 2]

The time period of simple harmonic motion of mass M in the given figure is π  where the value of α is _____

[31-Jan-2024 Shift 2]
Q.19 Correct
Q.19 In-correct
Q.19 Unattempt

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f1. The frequency of oscillations if a mass 9m is suspended from the same spring is f2. The value of f1/f2 is:

[1-Feb-2024 Shift 2]

A mass m is suspended from a spring of negligible mass and the system oscillates with a frequency f1. The frequency of oscillations if a mass 9m is suspended from the same spring is f2. The value of f1/f2 is:

[1-Feb-2024 Shift 2]
Q.20 Correct
Q.20 In-correct
Q.20 Unattempt
For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1‌kg, the angular frequency is ω1. When the mass block is 2‌kg the angular frequency is ω2. The ratio ω2∕ω1 is :

[30-Jan-2023 Shift 2]
For a simple harmonic motion in a mass spring system shown, the surface is frictionless. When the mass of the block is 1‌kg, the angular frequency is ω1. When the mass block is 2‌kg the angular frequency is ω2. The ratio ω2∕ω1 is :

[30-Jan-2023 Shift 2]
Q.21 Correct
Q.21 In-correct
Q.21 Unattempt
The velocity of a particle executing SHM varies with displacement (x) as 4v2=50−x2. The time period of oscillations is ‌
x
7
 s. The value of x is _______.
(‌ Take ‌π=‌
22
7
)
[30-Jan-2023 Shift 2]
The velocity of a particle executing SHM varies with displacement (x) as 4v2=50−x2. The time period of oscillations is ‌
x
7
 s. The value of x is _______.
(‌ Take ‌π=‌
22
7
)
[30-Jan-2023 Shift 2]
Q.22 Correct
Q.22 In-correct
Q.22 Unattempt
The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A ∕2, the kinetic energy of the block is
[31-Jan-2023 Shift 1]
The maximum potential energy of a block executing simple harmonic motion is 25 J. A is amplitude of oscillation. At A ∕2, the kinetic energy of the block is
[31-Jan-2023 Shift 1]
Q.23 Correct
Q.23 In-correct
Q.23 Unattempt
In the figure given below. a block of mass M=490g placed on a frictionless table is connected with two springs having same spring constant (K=2Nm−1). If the block is horizontally displaced through ' X 'm then the number of complete oscillations it will make in 14π seconds will be _______

[31-Jan-2023 Shift 1]
In the figure given below. a block of mass M=490g placed on a frictionless table is connected with two springs having same spring constant (K=2Nm−1). If the block is horizontally displaced through ' X 'm then the number of complete oscillations it will make in 14π seconds will be _______

[31-Jan-2023 Shift 1]
Q.24 Correct
Q.24 In-correct
Q.24 Unattempt
A particle executes simple harmonic motion between x=−A and x=+A. If time taken by particle to go from x=0 to ‌
A
2
 is 2 s; then time taken by particle in going from x=‌
A
2
 to A is :
[25-Jan-2023 Shift 2]
A particle executes simple harmonic motion between x=−A and x=+A. If time taken by particle to go from x=0 to ‌
A
2
 is 2 s; then time taken by particle in going from x=‌
A
2
 to A is :
[25-Jan-2023 Shift 2]
Q.25 Correct
Q.25 In-correct
Q.25 Unattempt
A particle of mass 250g executes a simple harmonic motion under a periodic force F=(−25 x) N. The particle attains a maximum speed of 4m∕ s during its oscillation. The amplitude of the motion is ________ cm.
[29-Jan-2023 Shift 2]
A particle of mass 250g executes a simple harmonic motion under a periodic force F=(−25 x) N. The particle attains a maximum speed of 4m∕ s during its oscillation. The amplitude of the motion is ________ cm.
[29-Jan-2023 Shift 2]
Q.26 Correct
Q.26 In-correct
Q.26 Unattempt
The general displacement of a simple harmonic oscillator is x=Asin‌ωt. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when t=‌
T
β
. The value of β is _______.
[30-Jan-2023 Shift 1]
The general displacement of a simple harmonic oscillator is x=Asin‌ωt. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when t=‌
T
β
. The value of β is _______.
[30-Jan-2023 Shift 1]
Q.27 Correct
Q.27 In-correct
Q.27 Unattempt
A block of mass 2‌kg is attached with two identical springs of spring constant 20N∕m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is ‌
π
√x
 in SI unit. The value of x is_____

[24-Jan-2023 Shift 1]
A block of mass 2‌kg is attached with two identical springs of spring constant 20N∕m each. The block is placed on a frictionless surface and the ends of the springs are attached to rigid supports (see figure). When the mass is displaced from its equilibrium position, it executes a simple harmonic motion. The time period of oscillation is ‌
π
√x
 in SI unit. The value of x is_____

[24-Jan-2023 Shift 1]
Q.28 Correct
Q.28 In-correct
Q.28 Unattempt
A body of mass 200g is tied to a spring of spring constant 12.5N∕m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5‌rad∕ s, then the ratio of extension in the spring to its natural length will be :
[24-Jan-2023 Shift 2]
A body of mass 200g is tied to a spring of spring constant 12.5N∕m, while the other end of spring is fixed at point O. If the body moves about O in a circular path on a smooth horizontal surface with constant angular speed 5‌rad∕ s, then the ratio of extension in the spring to its natural length will be :
[24-Jan-2023 Shift 2]
Q.29 Correct
Q.29 In-correct
Q.29 Unattempt
A mass m attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3‌kg the period of oscillation increases by one second, the value of mass m is ___kg.
[24-Jan-2023 Shift 2]
A mass m attached to free end of a spring executes SHM with a period of 1 s. If the mass is increased by 3‌kg the period of oscillation increases by one second, the value of mass m is ___kg.
[24-Jan-2023 Shift 2]
Q.30 Correct
Q.30 In-correct
Q.30 Unattempt
The general displacement of a simple harmonic oscillator is x=Asin‌ωt. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when t=‌
T
β
. The value of β is _______.
[30-Jan-2023 Shift 1]
The general displacement of a simple harmonic oscillator is x=Asin‌ωt. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when t=‌
T
β
. The value of β is _______.
[30-Jan-2023 Shift 1]
Q.31 Correct
Q.31 In-correct
Q.31 Unattempt
The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is:_______ cm.
[1-Feb-2023 Shift 1]
The amplitude of a particle executing SHM is 3 cm. The displacement at which its kinetic energy will be 25% more than the potential energy is:_______ cm.
[1-Feb-2023 Shift 1]
Q.32 Correct
Q.32 In-correct
Q.32 Unattempt
Choose the correct length (L) versus square of time period (T2) graph for a simple pendulum executing simple harmonic motion.
[1-Feb-2023 Shift 2]
Choose the correct length (L) versus square of time period (T2) graph for a simple pendulum executing simple harmonic motion.
[1-Feb-2023 Shift 2]
Q.33 Correct
Q.33 In-correct
Q.33 Unattempt
A simple pendulum with length 100‌cm and bob of mass 250g is executing S.H.M. of amplitude 10‌cm. The maximum tension in the string is found to be ‌
x
40
N. The value of x is _______.
[6-Apr-2023 shift 2]
A simple pendulum with length 100‌cm and bob of mass 250g is executing S.H.M. of amplitude 10‌cm. The maximum tension in the string is found to be ‌
x
40
N. The value of x is _______.
[6-Apr-2023 shift 2]
Q.34 Correct
Q.34 In-correct
Q.34 Unattempt
For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown in below figure, the projection of OP on the x-axis at time t is

[8-Apr-2023 shift 2]
For particle P revolving round the centre O with radius of circular path r and angular velocity ω, as shown in below figure, the projection of OP on the x-axis at time t is

[8-Apr-2023 shift 2]
Q.35 Correct
Q.35 In-correct
Q.35 Unattempt
A particle executes S.H.M. of amplitude A along x-axis. At t=0, the position of the particle is x=‌
A
2
 and it moves along positives x-axis. The displacement of particle in time t is x=Asin‌(ωt+δ), then the value δ will be
[10-Apr-2023 shift 1]
A particle executes S.H.M. of amplitude A along x-axis. At t=0, the position of the particle is x=‌
A
2
 and it moves along positives x-axis. The displacement of particle in time t is x=Asin‌(ωt+δ), then the value δ will be
[10-Apr-2023 shift 1]
Q.36 Correct
Q.36 In-correct
Q.36 Unattempt
A rectangular block of mass 5‌kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1m and time period 3.14 s. The maximum force exerted by spring on block is ________ N.
[10-Apr-2023 shift 2]
A rectangular block of mass 5‌kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1m and time period 3.14 s. The maximum force exerted by spring on block is ________ N.
[10-Apr-2023 shift 2]
Q.37 Correct
Q.37 In-correct
Q.37 Unattempt
The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by
[11-Apr-2023 shift 1]
The variation of kinetic energy (KE) of a particle executing simple harmonic motion with the displacement (x) starting from mean position to extreme position (A) is given by
[11-Apr-2023 shift 1]
Q.38 Correct
Q.38 In-correct
Q.38 Unattempt
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
[12-Apr-2023 shift 1]
A particle is executing simple harmonic motion (SHM). The ratio of potential energy and kinetic energy of the particle when its displacement is half of its amplitude will be
[12-Apr-2023 shift 1]
Q.39 Correct
Q.39 In-correct
Q.39 Unattempt
Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position?
[13-Apr-2023 shift 1]
Which graph represents the difference between total energy and potential energy of a particle executing SHM vs it's distance from mean position?
[13-Apr-2023 shift 1]
Q.40 Correct
Q.40 In-correct
Q.40 Unattempt
At a given point of time the value of displacement of a simple harmonic oscillator is given as y=A‌cos(30∘). If amplitude is 40‌cm and kinetic energy at that time is 200J, the value of force constant is 1.0×10xNm−1. The value of x is _______
[13-Apr-2023 shift 1]
At a given point of time the value of displacement of a simple harmonic oscillator is given as y=A‌cos(30∘). If amplitude is 40‌cm and kinetic energy at that time is 200J, the value of force constant is 1.0×10xNm−1. The value of x is _______
[13-Apr-2023 shift 1]
Q.41 Correct
Q.41 In-correct
Q.41 Unattempt
A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :
[13-Apr-2023 shift 2]
A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :
[13-Apr-2023 shift 2]
Q.42 Correct
Q.42 In-correct
Q.42 Unattempt
In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given below :
[15-Apr-2023 shift 1]
In a linear Simple Harmonic Motion (SHM)
(A) Restoring force is directly proportional to the displacement.
(B) The acceleration and displacement are opposite in direction.
(C) The velocity is maximum at mean position.
(D) The acceleration is minimum at extreme points.
Choose the correct answer from the options given below :
[15-Apr-2023 shift 1]
Q.43 Correct
Q.43 In-correct
Q.43 Unattempt
Two massless springs with spring constants 2k and 9k, carry 50g and 100g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:
[24-Jun-2022-Shift-2]
Two massless springs with spring constants 2k and 9k, carry 50g and 100g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be:
[24-Jun-2022-Shift-2]
Q.44 Correct
Q.44 In-correct
Q.44 Unattempt
The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :
[27-Jun-2022-Shift-1]
The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :
[27-Jun-2022-Shift-1]
Q.45 Correct
Q.45 In-correct
Q.45 Unattempt
The equation of a particle executing simple harmonic motion is given by x=sin‌π(t+‌
1
3
)‌m. At t=1s, the speed of particle will be
(Given : π=3.14 )
[27-Jun-2022-Shift-2]
The equation of a particle executing simple harmonic motion is given by x=sin‌π(t+‌
1
3
)‌m. At t=1s, the speed of particle will be
(Given : π=3.14 )
[27-Jun-2022-Shift-2]
Q.46 Correct
Q.46 In-correct
Q.46 Unattempt
A particle executes simple harmonic motion. Its amplitude is 8‌cm and time period is 6s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is s.
[27-Jun-2022-Shift-2]
A particle executes simple harmonic motion. Its amplitude is 8‌cm and time period is 6s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is s.
[27-Jun-2022-Shift-2]
Q.47 Correct
Q.47 In-correct
Q.47 Unattempt
A body is performing simple harmonic with an amplitude of 10‌cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is √x‌cm. The value of x is____
[29-Jun-2022-Shift-1]
A body is performing simple harmonic with an amplitude of 10‌cm. The velocity of the body was tripled by air jet when it is at 5 cm from its mean position. The new amplitude of vibration is √x‌cm. The value of x is____
[29-Jun-2022-Shift-1]
Q.48 Correct
Q.48 In-correct
Q.48 Unattempt
The motion of a simple pendulum executing S.H.M. is represented by the following equation.
y=A‌sin(πt+φ), where time is measured in second. The length of pendulum is
[29-Jun-2022-Shift-2]
The motion of a simple pendulum executing S.H.M. is represented by the following equation.
y=A‌sin(πt+φ), where time is measured in second. The length of pendulum is
[29-Jun-2022-Shift-2]
Q.49 Correct
Q.49 In-correct
Q.49 Unattempt
In figure (A), mass '2 m' is fixed on mass ' m ' which is attached to two springs of spring constant k. In figure (B), mass ' m ' is attached to two springs of spring constant ' k ' and ' 2k′. If mass ' m ' in (A) and in (B) are displaced by distance ' x ' horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.
[25-Jul-2022-Shift-1]

In figure (A), mass '2 m' is fixed on mass ' m ' which is attached to two springs of spring constant k. In figure (B), mass ' m ' is attached to two springs of spring constant ' k ' and ' 2k′. If mass ' m ' in (A) and in (B) are displaced by distance ' x ' horizontally and then released, then time period T1 and T2 corresponding to (A) and (B) respectively follow the relation.
[25-Jul-2022-Shift-1]
Q.50 Correct
Q.50 In-correct
Q.50 Unattempt
The length of a seconds pendulum at a height h=2R from earth surface will be:
(Given R= Radius of earth and acceleration due to gravity at the surface of earth, g=π2ms−2 )
[25-Jul-2022-Shift-2]
The length of a seconds pendulum at a height h=2R from earth surface will be:
(Given R= Radius of earth and acceleration due to gravity at the surface of earth, g=π2ms−2 )
[25-Jul-2022-Shift-2]
Q.51 Correct
Q.51 In-correct
Q.51 Unattempt
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is ____(degree).
[25-Jul-2022-Shift-2]
Two waves executing simple harmonic motions travelling in the same direction with same amplitude and frequency are superimposed. The resultant amplitude is equal to the √3 times of amplitude of individual motions. The phase difference between the two motions is ____(degree).
[25-Jul-2022-Shift-2]
Q.52 Correct
Q.52 In-correct
Q.52 Unattempt
When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :
[26-Jul-2022-Shift-1]
When a particle executes Simple Hormonic Motion, the nature of graph of velocity as a function of displacement will be :
[26-Jul-2022-Shift-1]
Q.53 Correct
Q.53 In-correct
Q.53 Unattempt
As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a) is 3s, then the period of oscillation in figure (b) will be √xs. The value of x is ________.

[26-Jul-2022-Shift-2]
As per given figures, two springs of spring constants k and 2k are connected to mass m. If the period of oscillation in figure (a) is 3s, then the period of oscillation in figure (b) will be √xs. The value of x is ________.

[26-Jul-2022-Shift-2]
Q.54 Correct
Q.54 In-correct
Q.54 Unattempt
Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge q0 with mass ' m ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0 executes SHM. The time period of oscillation of charge q0 will be :
[27-Jul-2022-Shift-1]
Two identical positive charges Q each are fixed at a distance of '2a' apart from each other. Another point charge q0 with mass ' m ' is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge q0 executes SHM. The time period of oscillation of charge q0 will be :
[27-Jul-2022-Shift-1]
Q.55 Correct
Q.55 In-correct
Q.55 Unattempt
Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3s and 4s respectively. If their moments of inertia are in the ratio of 3:2, then the ratio of their magnetic moments will be:
[27-Jul-2022-Shift-1]
Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of 3s and 4s respectively. If their moments of inertia are in the ratio of 3:2, then the ratio of their magnetic moments will be:
[27-Jul-2022-Shift-1]
Q.56 Correct
Q.56 In-correct
Q.56 Unattempt
A mass 0.9‌kg, attached to a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124g is placed over it and both masses move together with amplitude A2. If the ratio ‌
A1
A2
 is ‌
α
α−1
, then the value of α will be ________.
[27-Jul-2022-Shift-1]
A mass 0.9‌kg, attached to a horizontal spring, executes SHM with an amplitude A1. When this mass passes through its mean position, then a smaller mass of 124g is placed over it and both masses move together with amplitude A2. If the ratio ‌
A1
A2
 is ‌
α
α−1
, then the value of α will be ________.
[27-Jul-2022-Shift-1]
Q.57 Correct
Q.57 In-correct
Q.57 Unattempt
A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip‌30∘. The number of oscillations per minute become 10 at another place Q of 60∘ dip. The ratio of the total magnetic field at the two places (BQ:BP) is :
[27-Jul-2022-Shift-2]
A compass needle of oscillation magnetometer oscillates 20 times per minute at a place P of dip‌30∘. The number of oscillations per minute become 10 at another place Q of 60∘ dip. The ratio of the total magnetic field at the two places (BQ:BP) is :
[27-Jul-2022-Shift-2]
Q.58 Correct
Q.58 In-correct
Q.58 Unattempt
The potential energy of a particle of mass 4‌kg in motion along the x-axis is given by U=4(1−cos‌4‌x)J. The time period of the particle for small oscillation ( sinθ≃θ) is (‌
π
K
)s. The value of K is ________.
[28-Jul-2022-Shift-2]
The potential energy of a particle of mass 4‌kg in motion along the x-axis is given by U=4(1−cos‌4‌x)J. The time period of the particle for small oscillation ( sinθ≃θ) is (‌
π
K
)s. The value of K is ________.
[28-Jul-2022-Shift-2]
Q.59 Correct
Q.59 In-correct
Q.59 Unattempt
The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by :
[29-Jul-2022-Shift-1]
The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination α, is given by :
[29-Jul-2022-Shift-1]
Q.60 Correct
Q.60 In-correct
Q.60 Unattempt
The metallic bob of simple pendulum has the relative density 5 . The time period of this pendulum is 10s. If the metallic bob is immersed in water, then the new time period becomes 5√xs. The value of x will be ______.
[29-Jul-2022-Shift-2]
The metallic bob of simple pendulum has the relative density 5 . The time period of this pendulum is 10s. If the metallic bob is immersed in water, then the new time period becomes 5√xs. The value of x will be ______.
[29-Jul-2022-Shift-2]
Q.61 Correct
Q.61 In-correct
Q.61 Unattempt
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is
[24 Feb 2021 Shift 2]
When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is
[24 Feb 2021 Shift 2]
Q.62 Correct
Q.62 In-correct
Q.62 Unattempt
Given below are two statements:
Statement I A second's pendulum has a time period of 1s.
Statement II It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below.
[26 Feb 2021 Shift 2]
Given below are two statements:
Statement I A second's pendulum has a time period of 1s.
Statement II It takes precisely one second to move between the two extreme positions.
In the light of the above statements, choose the correct answer from the options given below.
[26 Feb 2021 Shift 2]
Q.63 Correct
Q.63 In-correct
Q.63 Unattempt
Time period of a simple pendulum is T. The time taken to complete 5∕8 oscillations starting from mean position is ‌
α
β
T. The value of α is ......... .
[26 Feb 2021 Shift 2]
Time period of a simple pendulum is T. The time taken to complete 5∕8 oscillations starting from mean position is ‌
α
β
T. The value of α is ......... .
[26 Feb 2021 Shift 2]
Q.64 Correct
Q.64 In-correct
Q.64 Unattempt
If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor
[26 Feb 2021 Shift 1]
If two similar springs each of spring constant K1 are joined in series, the new spring constant and time period would be changed by a factor
[26 Feb 2021 Shift 1]
Q.65 Correct
Q.65 In-correct
Q.65 Unattempt
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (‌
R
2
) from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period?
[26 Feb 2021 Shift 1]
Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance (‌
R
2
) from the earth's centre, where R is the radius of the earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simple harmonic motion with a time period?
[26 Feb 2021 Shift 1]
Q.66 Correct
Q.66 In-correct
Q.66 Unattempt
Two identical springs of spring constant 2k are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is

[25 Feb 2021 Shift 2]
Two identical springs of spring constant 2k are attached to a block of mass m and to fixed support (see figure). When the mass is displaced from equilibrium position on either side, it executes simple harmonic motion. The time period of oscillations of this system is

[25 Feb 2021 Shift 2]
Q.67 Correct
Q.67 In-correct
Q.67 Unattempt
If the time period of a 2m long simple pendulum is 2s, the acceleration due to gravity at the place, where pendulum is executing SHM is
[25 Feb 2021 Shift 1]
If the time period of a 2m long simple pendulum is 2s, the acceleration due to gravity at the place, where pendulum is executing SHM is
[25 Feb 2021 Shift 1]
Q.68 Correct
Q.68 In-correct
Q.68 Unattempt
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, then the frequency of oscillation of given body is

[24 Feb 2021 Shift 2]
In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, then the frequency of oscillation of given body is

[24 Feb 2021 Shift 2]
Q.69 Correct
Q.69 In-correct
Q.69 Unattempt
A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin, i.e. ma=−αx2. The distance at which the particle stops is
[24 Feb 2021 Shift 2]
A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin, i.e. ma=−αx2. The distance at which the particle stops is
[24 Feb 2021 Shift 2]
Q.70 Correct
Q.70 In-correct
Q.70 Unattempt
A student is performing the experiment of resonance column. The diameter of the column tube is 6cm. The frequency of the tuning fork is 504Hz. Speed of the sound at the given temperature is 336m∕s. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is
[25 Feb 2021 Shift 1]
A student is performing the experiment of resonance column. The diameter of the column tube is 6cm. The frequency of the tuning fork is 504Hz. Speed of the sound at the given temperature is 336m∕s. The zero of the meter scale coincides with the top end of the resonance column tube. The reading of the water level in the column when the first resonance occurs is
[25 Feb 2021 Shift 1]
Q.71 Correct
Q.71 In-correct
Q.71 Unattempt
A particle executes SHM, the graph of velocity as a function of displacement is
[26 Feb 2021 Shift 2]
A particle executes SHM, the graph of velocity as a function of displacement is
[26 Feb 2021 Shift 2]
Q.72 Correct
Q.72 In-correct
Q.72 Unattempt
A particle executes SHM with amplitude a and time period T. The displacement of the particle when its speed is half of maximum speed is ‌
√xa
2
. The value of x is ........... .
[26 Feb 2021 Shift 2]
A particle executes SHM with amplitude a and time period T. The displacement of the particle when its speed is half of maximum speed is ‌
√xa
2
. The value of x is ........... .
[26 Feb 2021 Shift 2]
Q.73 Correct
Q.73 In-correct
Q.73 Unattempt
Y=A‌sin(ωt+φ0) is the time-displacement equation of SHM. At t=0, the displacement of the particle is Y=‌
A
2
 and it is moving along negative x-direction. Then, the initial phase angle φ0 will be
[25 Feb 2021 Shift 2]
Y=A‌sin(ωt+φ0) is the time-displacement equation of SHM. At t=0, the displacement of the particle is Y=‌
A
2
 and it is moving along negative x-direction. Then, the initial phase angle φ0 will be
[25 Feb 2021 Shift 2]
Q.74 Correct
Q.74 In-correct
Q.74 Unattempt
The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and covers 30∘ in 0.1s. The perpendicular projection P from A on the diameter MN represents the simple harmonic motion of P. The restoration force per unit mass when P touches M will be

[25 Feb 2021 Shift 2]
The point A moves with a uniform speed along the circumference of a circle of radius 0.36m and covers 30∘ in 0.1s. The perpendicular projection P from A on the diameter MN represents the simple harmonic motion of P. The restoration force per unit mass when P touches M will be

[25 Feb 2021 Shift 2]
Q.75 Correct
Q.75 In-correct
Q.75 Unattempt
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be :

[24feb2021shift1]
In the given figure, a mass M is attached to a horizontal spring which is fixed on one side to a rigid support. The spring constant of the spring is k. The mass oscillates on a frictionless surface with time period T and amplitude A. When the mass is in equilibrium position, as shown in the figure, another mass m is gently fixed upon it. The new amplitude of oscillation will be :

[24feb2021shift1]
Q.76 Correct
Q.76 In-correct
Q.76 Unattempt
Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is
[17 Mar 2021 Shift 2]
Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities during oscillations are equal, the ratio of the amplitude of A and B is
[17 Mar 2021 Shift 2]
Q.77 Correct
Q.77 In-correct
Q.77 Unattempt
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig.1 shows one of them and Fig.2 shows their series combination. The ratios of time period of oscillation of the two SHM is ‌
Tb
Ta
=√x, where value of x is .........
(Round off to the nearest integer)

[17 Mar 2021 Shift 1]
Consider two identical springs each of spring constant k and negligible mass compared to the mass M as shown. Fig.1 shows one of them and Fig.2 shows their series combination. The ratios of time period of oscillation of the two SHM is ‌
Tb
Ta
=√x, where value of x is .........
(Round off to the nearest integer)

[17 Mar 2021 Shift 1]
Q.78 Correct
Q.78 In-correct
Q.78 Unattempt
Time period of a simple pendulum is T inside a lift, when the lift is stationary. If the lift moves upwards with an acceleration g/2, then the time period of pendulum will be
[16 Mar 2021 Shift 1]
Time period of a simple pendulum is T inside a lift, when the lift is stationary. If the lift moves upwards with an acceleration g/2, then the time period of pendulum will be
[16 Mar 2021 Shift 1]
Q.79 Correct
Q.79 In-correct
Q.79 Unattempt
A block of mass 1kg attached to a spring is made to oscillate with an initial amplitude of 12cm. After 2min, the amplitude decreases to 6cm. Determine the value of the damping constant for this motion.
(Take, In 2=0.693 )
[17 Mar 2021 Shift 2]
A block of mass 1kg attached to a spring is made to oscillate with an initial amplitude of 12cm. After 2min, the amplitude decreases to 6cm. Determine the value of the damping constant for this motion.
(Take, In 2=0.693 )
[17 Mar 2021 Shift 2]
Q.80 Correct
Q.80 In-correct
Q.80 Unattempt
The function of time representing a simple harmonic motion with a period of ‌
π
ω
 is
[18 Mar 2021 Shift 2]
The function of time representing a simple harmonic motion with a period of ‌
π
ω
 is
[18 Mar 2021 Shift 2]
Q.81 Correct
Q.81 In-correct
Q.81 Unattempt
A particle performs simple harmonic motion with a period of 2s. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is
1
a
s. The value of a to the nearest integer is
[18 Mar 2021 Shift 1]
A particle performs simple harmonic motion with a period of 2s. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is
1
a
s. The value of a to the nearest integer is
[18 Mar 2021 Shift 1]
Q.82 Correct
Q.82 In-correct
Q.82 Unattempt
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
[17 Mar 2021 Shift 1]
For what value of displacement the kinetic energy and potential energy of a simple harmonic oscillation become equal?
[17 Mar 2021 Shift 1]
Q.83 Correct
Q.83 In-correct
Q.83 Unattempt
In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rad/s when k = 20 N/m.

[25 Jul 2021 Shift 1]
In the reported figure, two bodies A and B of masses 200 g and 800 g are attached with the system of springs. Springs are kept in a stretched position with some extension when the system is released. The horizontal surface is assumed to be frictionless. The angular frequency will be _______ rad/s when k = 20 N/m.

[25 Jul 2021 Shift 1]
Q.84 Correct
Q.84 In-correct
Q.84 Unattempt
T0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to‌
1
16
 times of its initial value, the modified timeperiod is :
[22 Jul 2021 Shift 2]
T0 is the time period of a simple pendulum at a place. If the length of the pendulum is reduced to‌
1
16
 times of its initial value, the modified timeperiod is :
[22 Jul 2021 Shift 2]
Q.85 Correct
Q.85 In-correct
Q.85 Unattempt
The motion of a mass on a spring, with spring constant K is as shown in figure.
The equation of motion is given by x(t)= Asin\ω t+ Bcos\ωtwith ω=√
K
m
Suppose that at time t=0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t)=C‌cos(ωt−ϕ), where Cand ϕ are :
[22 Jul 2021 Shift 2]
The motion of a mass on a spring, with spring constant K is as shown in figure.

The equation of motion is given by x(t)= Asin\ω t+ Bcos\ωtwith ω=√
K
m
Suppose that at time t=0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t)=C‌cos(ωt−ϕ), where Cand ϕ are :
[22 Jul 2021 Shift 2]
Q.86 Correct
Q.86 In-correct
Q.86 Unattempt
A particle executes simple harmonic motion represented by displacement function as
x(t)=A‌sin(ωt+ϕ)
If the position and velocity of the particle at t=0s are 2cm and 2ωcms−1 respectively, then its amplitude is x√2cm where the value of x is ____.
[27 Jul 2021 Shift 2]
A particle executes simple harmonic motion represented by displacement function as
x(t)=A‌sin(ωt+ϕ)
If the position and velocity of the particle at t=0s are 2cm and 2ωcms−1 respectively, then its amplitude is x√2cm where the value of x is ____.
[27 Jul 2021 Shift 2]
Q.87 Correct
Q.87 In-correct
Q.87 Unattempt
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is
3E
4
 then its displacement 'y' is given by:
[27 Jul 2021 Shift 1]
A particle starts executing simple harmonic motion (SHM) of amplitude 'a' and total energy E. At any instant, its kinetic energy is
3E
4
 then its displacement 'y' is given by:
[27 Jul 2021 Shift 1]
Q.88 Correct
Q.88 In-correct
Q.88 Unattempt
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
[25 Jul 2021 Shift 2]
In a simple harmonic oscillation, what fraction of total mechanical energy is in the form of kinetic energy, when the particle is midway between mean and extreme position.
[25 Jul 2021 Shift 2]
Q.89 Correct
Q.89 In-correct
Q.89 Unattempt
A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as:
[20 Jul 2021 Shift 2]
A particle is making simple harmonic motion along the X-axis. If at a distances x1 and x2 from the mean position the velocities of the particle are v1 and v2 respectively. The time period of its oscillation is given as:
[20 Jul 2021 Shift 2]
Q.90 Correct
Q.90 In-correct
Q.90 Unattempt
A particle of mass 1‌kg is hanging from a spring of force constant 100Nm−1. The mass is pulled slightly downward and released, so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is
T
x
. The value of x is.
[31 Aug 2021 Shift 1]
A particle of mass 1‌kg is hanging from a spring of force constant 100Nm−1. The mass is pulled slightly downward and released, so that it executes free simple harmonic motion with time period T. The time when the kinetic energy and potential energy of the system will become equal, is
T
x
. The value of x is.
[31 Aug 2021 Shift 1]
Q.91 Correct
Q.91 In-correct
Q.91 Unattempt
A bob of mass m suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density
1
4
 times that of the bob and the length of the thread is increased by
1
3
‌rd of the original length, then the time period of the simple harmonic oscillations will be
[31 Aug 2021 Shift 2]
A bob of mass m suspended by a thread of length l undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density
1
4
 times that of the bob and the length of the thread is increased by
1
3
‌rd of the original length, then the time period of the simple harmonic oscillations will be
[31 Aug 2021 Shift 2]
Q.92 Correct
Q.92 In-correct
Q.92 Unattempt
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass m to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as ..........%.
[26 Aug 2021 Shift 2]
The acceleration due to gravity is found upto an accuracy of 4% on a planet. The energy supplied to a simple pendulum to known mass m to undertake oscillations of time period T is being estimated. If time period is measured to an accuracy of 3%, the accuracy to which E is known as ..........%.
[26 Aug 2021 Shift 2]
Q.93 Correct
Q.93 In-correct
Q.93 Unattempt
For a body executing SHM
A. potential energy is always equal to its kinetic energy.
B. average potential and kinetic energy over any given time interval are always equal.
C. sum of the kinetic and potential energy at any point of time is constant.
D. average kinetic energy in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below.
[31 Aug 2021 Shift 2]
For a body executing SHM
A. potential energy is always equal to its kinetic energy.
B. average potential and kinetic energy over any given time interval are always equal.
C. sum of the kinetic and potential energy at any point of time is constant.
D. average kinetic energy in one time period is equal to average potential energy in one time period.
Choose the most appropriate option from the options given below.
[31 Aug 2021 Shift 2]
Q.94 Correct
Q.94 In-correct
Q.94 Unattempt
Two simple harmonic motion, are represented by the equations y1=10 sin(3πt+
π
3
) and y2=5(sin‌3‌π‌t+√3‌cos‌3‌π‌t) Ratio of amplitude of y1 to y2=x:1. The value of x is ............ .
[27 Aug 2021 Shift 2]
Two simple harmonic motion, are represented by the equations y1=10 sin(3πt+
π
3
) and y2=5(sin‌3‌π‌t+√3‌cos‌3‌π‌t) Ratio of amplitude of y1 to y2=x:1. The value of x is ............ .
[27 Aug 2021 Shift 2]
Q.95 Correct
Q.95 In-correct
Q.95 Unattempt
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.
The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :
[27 Aug 2021 Shift 1]
The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

The potential energy U(x) versus time (t) plot of the particle is correctly shown in figure :
[27 Aug 2021 Shift 1]
Q.96 Correct
Q.96 In-correct
Q.96 Unattempt
Two simple harmonic motions are represented by the equations
x1=5‌sin(2πt+
π
4
) and
x2=5√2(sin‌2‌π‌t+cos‌2‌π‌t)
The amplitude of second motion is ..............times the amplitude in first motion.
[26 Aug 2021 Shift 2]
Two simple harmonic motions are represented by the equations
x1=5‌sin(2πt+
π
4
) and
x2=5√2(sin‌2‌π‌t+cos‌2‌π‌t)
The amplitude of second motion is ..............times the amplitude in first motion.
[26 Aug 2021 Shift 2]
Q.97 Correct
Q.97 In-correct
Q.97 Unattempt
A mass of 5‌kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure. A simple pendulum of length 4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?
[1 Sep 2021 Shift 2]
A mass of 5‌kg is connected to a spring. The potential energy curve of the simple harmonic motion executed by the system is shown in the figure.  A simple pendulum of length 4m has the same period of oscillation as the spring system. What is the value of acceleration due to gravity on the planet where these experiments are performed?
[1 Sep 2021 Shift 2]
Q.98 Correct
Q.98 In-correct
Q.98 Unattempt
The displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)
Which of the following statements is/are true for this motion?
(1) The force is zero at t=
3T
4
(2) The acceleration is maximum at t=T
(3) The speed is maximum at t=
T
4
(4) The P.E. is equal to K.E. of the oscillation at t=
T
2
[Sep. 02, 2020 (II)]
The displacement time graph of a particle executing S.H.M. is given in figure : (sketch is schematic and not to scale)

Which of the following statements is/are true for this motion?
(1) The force is zero at t=
3T
4
(2) The acceleration is maximum at t=T
(3) The speed is maximum at t=
T
4
(4) The P.E. is equal to K.E. of the oscillation at t=
T
2
[Sep. 02, 2020 (II)]
Q.99 Correct
Q.99 In-correct
Q.99 Unattempt
An object of mass m is suspended at the end of a massless wire of length L and area of cross-section, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:
[Sep. 06, 2020 (I)]
An object of mass m is suspended at the end of a massless wire of length L and area of cross-section, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:
[Sep. 06, 2020 (I)]
Q.100 Correct
Q.100 In-correct
Q.100 Unattempt
When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t)=y0sin2ωt, where ′y′ is measured from the lower end of unstretched spring. Then ω is:
[Sep. 06, 2020 (II)]
When a particle of mass m is attached to a vertical spring of spring constant k and released, its motion is described by y(t)=y0sin2ωt, where ′y′ is measured from the lower end of unstretched spring. Then ω is:
[Sep. 06, 2020 (II)]
Q.101 Correct
Q.101 In-correct
Q.101 Unattempt
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is :
[Sep. 03, 2020 (II)]
A block of mass m attached to a massless spring is performing oscillatory motion of amplitude 'A' on a frictionless horizontal plane. If half of the mass of the block breaks off when it is passing through its equilibrium point, the amplitude of oscillation for the remaining system become fA. The value of f is :
[Sep. 03, 2020 (II)]
Q.102 Correct
Q.102 In-correct
Q.102 Unattempt
The position co-ordinates of a particle moving in a 3−D coordinate system is given by
x=a‌cos‌ω‌t
y=a‌sin‌ω‌t
and z=aωt
The speed of the particle is:
[9 Jan 2019, II]
The position co-ordinates of a particle moving in a 3−D coordinate system is given by
x=a‌cos‌ω‌t
y=a‌sin‌ω‌t
and z=aωt
The speed of the particle is:
[9 Jan 2019, II]
Q.103 Correct
Q.103 In-correct
Q.103 Unattempt
A particle undergoing simple harmonic motion has time dependent displacement given by x(t)=A‌sin‌
πt
90
. The ratio of kinetic to potential energy of this particle at t=210s will be
[11 Jan 2019, I]
A particle undergoing simple harmonic motion has time dependent displacement given by x(t)=A‌sin‌
πt
90
. The ratio of kinetic to potential energy of this particle at t=210s will be
[11 Jan 2019, I]
Q.104 Correct
Q.104 In-correct
Q.104 Unattempt
A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2.
[11 Jan 2019, II]
A pendulum is executing simple harmonic motion and its maximum kinetic energy is K1. If the length of the pendulum is doubled and it performs simple harmonic motion with the same amplitude as in the first case, its maximum kinetic energy is K2.
[11 Jan 2019, II]
Q.105 Correct
Q.105 In-correct
Q.105 Unattempt
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x -axis, about x=0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:
[9 Jan 2019, II]
A particle is executing simple harmonic motion (SHM) of amplitude A, along the x -axis, about x=0. When its potential Energy (PE) equals kinetic energy (KE), the position of the particle will be:
[9 Jan 2019, II]
Q.106 Correct
Q.106 In-correct
Q.106 Unattempt
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre ' O ' and can rotate frreely in horizontal plane. The other ends of two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:

[12 Jan 2019, I]
Two light identical springs of spring constant k are attached horizontally at the two ends of a uniform horizontal rod AB of length l and mass m. The rod is pivoted at its centre ' O ' and can rotate frreely in horizontal plane. The other ends of two springs are fixed to rigid supports as shown in figure. The rod is gently pushed through a small angle and released. The frequency of resulting oscillation is:

[12 Jan 2019, I]
Q.107 Correct
Q.107 In-correct
Q.107 Unattempt
A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. The M is given by:
[12 Jan 2019, I]
A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on a horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. The M is given by:
[12 Jan 2019, I]
Q.108 Correct
Q.108 In-correct
Q.108 Unattempt
A simple harmonic motion is represented by
y=5(sin‌3‌π‌t+√3‌cos‌3‌π‌t)cm
The amplitude and time period of the motion are :
[12 Jan 2019, II]
A simple harmonic motion is represented by
y=5(sin‌3‌π‌t+√3‌cos‌3‌π‌t)cm
The amplitude and time period of the motion are :
[12 Jan 2019, II]
Q.109 Correct
Q.109 In-correct
Q.109 Unattempt
A simple pendulum of length 1m is oscillating with an angular frequency 10‌rad∕s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1rad∕s and an amplitude of 10−2m. The relative change in the angular frequency of the pendulum is best given by:
[11 Jan 2019, II]
A simple pendulum of length 1m is oscillating with an angular frequency 10‌rad∕s. The support of the pendulum starts oscillating up and down with a small angular frequency of 1rad∕s and an amplitude of 10−2m. The relative change in the angular frequency of the pendulum is best given by:
[11 Jan 2019, II]
Q.110 Correct
Q.110 In-correct
Q.110 Unattempt
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be:
[11 Jan 2019, II]
The mass and the diameter of a planet are three times the respective values for the Earth. The period of oscillation of a simple pendulum on the Earth is 2s. The period of oscillation of the same pendulum on the planet would be:
[11 Jan 2019, II]
Q.111 Correct
Q.111 In-correct
Q.111 Unattempt
A particle executes simple harmonic motion with an amplitude of 5cm. When the particle is at 4cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:
[10 Jan 2019, II]
A particle executes simple harmonic motion with an amplitude of 5cm. When the particle is at 4cm from the mean position, the magnitude of its velocity in SI units is equal to that of its acceleration. Then, its periodic time in seconds is:
[10 Jan 2019, II]
Q.112 Correct
Q.112 In-correct
Q.112 Unattempt
A cylindrical plastic bottle of negligible mass is filled with 310ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5cm then omega is close to: (density of water =103kg∕m3 )
[10 Jan 2019, II]
A cylindrical plastic bottle of negligible mass is filled with 310ml of water and left floating in a pond with still water. If pressed downward slightly and released, it starts performing simple harmonic motion at angular frequency ω. If the radius of the bottle is 2.5cm then omega is close to: (density of water =103kg∕m3 )
[10 Jan 2019, II]
Q.113 Correct
Q.113 In-correct
Q.113 Unattempt
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m∕M is close to :
[9 Jan 2019, II]
A rod of mass 'M' and length '2L' is suspended at its middle by a wire. It exhibits torsional oscillations; If two masses each of 'm' are attached at distance 'L/2' from its centre on both sides, it reduces the oscillation frequency by 20%. The value of ratio m∕M is close to :
[9 Jan 2019, II]
Q.114 Correct
Q.114 In-correct
Q.114 Unattempt
The displacement of a damped harmonic oscillator is given by x(t)=e0.1t.cos(10πt+φ). Here tis in seconds.
The time taken for its amplitude of vibration to drop to half of its initial value is close to :
[9 Jan 2019, II]
The displacement of a damped harmonic oscillator is given by x(t)=e0.1t.cos(10πt+φ). Here tis in seconds.
The time taken for its amplitude of vibration to drop to half of its initial value is close to :
[9 Jan 2019, II]
Q.115 Correct
Q.115 In-correct
Q.115 Unattempt
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l(l<<L), is close to :
[12 April 2019, II]
A person of mass M is, sitting on a swing of length L and swinging with an angular amplitude θ0. If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance l(l<<L), is close to :
[12 April 2019, II]
Q.116 Correct
Q.116 In-correct
Q.116 Unattempt
A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is
1
16
 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :
[9 April 2019 I]
A simple pendulum oscillating in air has period T. The bob of the pendulum is completely immersed in a non-viscous liquid. The density of the liquid is
1
16
 th of the material of the bob. If the bob is inside liquid all the time, its period of oscillation in this liquid is :
[9 April 2019 I]
Q.117 Correct
Q.117 In-correct
Q.117 Unattempt
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to
1
1000
 of the original amplitude is close to:
[8 April 2019, II]
A damped harmonic oscillator has a frequency of 5 oscillations per second. The amplitude drops to half its value for every 10 oscillations. The time it will take to drop to
1
1000
 of the original amplitude is close to:
[8 April 2019, II]
Q.118 Correct
Q.118 In-correct
Q.118 Unattempt
Two simple harmonic motions, as shown, are at right angles.
They are combined to form Lissajous figures.
x(t)=A‌sin(at+δ)
y(t)=B‌sin(bt)
Identify the correct match below
[Online April 15, 2018]
Two simple harmonic motions, as shown, are at right angles.
They are combined to form Lissajous figures.
x(t)=A‌sin(at+δ)
y(t)=B‌sin(bt)
Identify the correct match below
[Online April 15, 2018]
Q.119 Correct
Q.119 In-correct
Q.119 Unattempt
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012∕sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver =108 and Avagadro number =6.02×1023gmmole−1)
[2018]
A silver atom in a solid oscillates in simple harmonic motion in some direction with a frequency of 1012∕sec. What is the force constant of the bonds connecting one atom with the other? (Mole wt. of silver =108 and Avagadro number =6.02×1023gmmole−1)
[2018]
Q.120 Correct
Q.120 In-correct
Q.120 Unattempt
A particle executes simple harmonic motion and is located at x=a,b and c at ×t0,2t0 and 3t0 respectively. The frequency of the oscillation is
[Online April 16, 2018]
A particle executes simple harmonic motion and is located at x=a,b and c at ×t0,2t0 and 3t0 respectively. The frequency of the oscillation is
[Online April 16, 2018]
Q.121 Correct
Q.121 In-correct
Q.121 Unattempt
An oscillator of mass M is at rest in its equilibrium position in a potential V=
1
2
k(x−X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is:
(M=10,m=5,u=1,k=1),
[Online April 16, 2018]
An oscillator of mass M is at rest in its equilibrium position in a potential V=
1
2
k(x−X)2. A particle of mass m comes from right with speed u and collides completely inelastically with M and sticks to it. This process repeats every time the oscillator crosses its equilibrium position. The amplitude of oscillations after 13 collisions is:
(M=10,m=5,u=1,k=1),
[Online April 16, 2018]
Q.122 Correct
Q.122 In-correct
Q.122 Unattempt
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10s−1. At, t=0 the displacement is 5m. What is the maximum acceleration ? The initial phase is
π
4
[Online April 8,2017]
The ratio of maximum acceleration to maximum velocity in a simple harmonic motion is 10s−1. At, t=0 the displacement is 5m. What is the maximum acceleration ? The initial phase is
π
4
[Online April 8,2017]
Q.123 Correct
Q.123 In-correct
Q.123 Unattempt
A particle is executing simple harmonic motion with a time period T. At time t=0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like:
[2017]
A particle is executing simple harmonic motion with a time period T. At time t=0, it is at its position of equilibrium. The kinetic energy-time graph of the particle will look like:
[2017]
Q.124 Correct
Q.124 In-correct
Q.124 Unattempt
A block of mass 0.1kg is connected to an elastic spring of spring constant 640Nm−1 and oscillates in a medium of constant 10−2kgs−1. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :
[Online April 9,2017]
A block of mass 0.1kg is connected to an elastic spring of spring constant 640Nm−1 and oscillates in a medium of constant 10−2kgs−1. The system dissipates its energy gradually. The time taken for its mechanical energy of vibration to drop to half of its initial value, is closest to :
[Online April 9,2017]
Q.125 Correct
Q.125 In-correct
Q.125 Unattempt
In an experiment to determine the period of a simple pendulum of length 1m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uni- form mass distribution. If the relative difference in the periods, is found to be 5×10−4s, the difference in radii, |r1−r2| is best given by:
[Online April 9,2017]
In an experiment to determine the period of a simple pendulum of length 1m, it is attached to different spherical bobs of radii r1 and r2. The two spherical bobs have uni- form mass distribution. If the relative difference in the periods, is found to be 5×10−4s, the difference in radii, |r1−r2| is best given by:
[Online April 9,2017]
Q.126 Correct
Q.126 In-correct
Q.126 Unattempt
A 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8kg block placed on the same table. So, the frequency of vibration of the 8kg block is :
[Online April 8, 2017]
A 1kg block attached to a spring vibrates with a frequency of 1Hz on a frictionless horizontal table. Two springs identical to the original spring are attached in parallel to an 8kg block placed on the same table. So, the frequency of vibration of the 8kg block is :
[Online April 8, 2017]
Q.127 Correct
Q.127 In-correct
Q.127 Unattempt
A particle performs simple harmonic mition with amplitude A. Its speed is trebled at the instant that it is at a distance
2A
3
 from equilibrium position. The new amplitude of the motion is:
[2016]
A particle performs simple harmonic mition with amplitude A. Its speed is trebled at the instant that it is at a distance
2A
3
 from equilibrium position. The new amplitude of the motion is:
[2016]
Q.128 Correct
Q.128 In-correct
Q.128 Unattempt
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t=0 one particle has displacement A while the other one has displacement
−A
2
 and they are moving towards each other. If they cross each other at time t, then t is:
[Online April 9, 2016]
Two particles are performing simple harmonic motion in a straight line about the same equilibrium point. The amplitude and time period for both particles are same and equal to A and T, respectively. At time t=0 one particle has displacement A while the other one has displacement
−A
2
 and they are moving towards each other. If they cross each other at time t, then t is:
[Online April 9, 2016]
Q.129 Correct
Q.129 In-correct
Q.129 Unattempt
A pendulum clock loses 12s a day if the temperature is 40°C and gains 4s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively:
[2016]
A pendulum clock loses 12s a day if the temperature is 40°C and gains 4s a day if the temperature is 20°C. The temperature at which the clock will show correct time, and the co-efficient of linear expansion (α) of the metal of the pendulum shaft are respectively:
[2016]
Q.130 Correct
Q.130 In-correct
Q.130 Unattempt
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :
[Online April 10,2016]
In an engine the piston undergoes vertical simple harmonic motion with amplitude 7cm. A washer rests on top of the piston and moves with it. The motor speed is slowly increased. The frequency of the piston at which the washer no longer stays in contact with the piston, is close to :
[Online April 10,2016]
Q.131 Correct
Q.131 In-correct
Q.131 Unattempt
A simple harmonic oscillator of angular frequency 2rad s−1 is acted upon by an external force F=sin‌t‌N. If the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to:
[Online April 10, 2015]
A simple harmonic oscillator of angular frequency 2rad s−1 is acted upon by an external force F=sin‌t‌N. If the oscillator is at rest in its equilibrium position at t=0, its position at later times is proportional to:
[Online April 10, 2015]
Q.132 Correct
Q.132 In-correct
Q.132 Unattempt
x and y displacements of a particle are given as x(t)=a‌sin ω t and y(t)=a‌sin‌2‌ω‌t. Its trajectory will look like:
[Online April 10, 2015]
x and y displacements of a particle are given as x(t)=a‌sin ω t and y(t)=a‌sin‌2‌ω‌t. Its trajectory will look like:
[Online April 10, 2015]
Q.133 Correct
Q.133 In-correct
Q.133 Unattempt
For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
[2015]
For a simple pendulum, a graph is plotted between its kinetic energy (KE) and potential energy (PE) against its displacement d. Which one of the following represents these correctly? (graphs are schematic and not drawn to scale)
[2015]
Q.134 Correct
Q.134 In-correct
Q.134 Unattempt
A pendulum with time period of 1s is losing energy. At certain time its energy is 45J. If after completing 15 oscillations, its energy has become 15J, its damping constant (in s−1 ) is :
[Online April 11, 2015]
A pendulum with time period of 1s is losing energy. At certain time its energy is 45J. If after completing 15 oscillations, its energy has become 15J, its damping constant (in s−1 ) is :
[Online April 11, 2015]
Q.135 Correct
Q.135 In-correct
Q.135 Unattempt
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM. If the Young's modulus of the material of the wire is Y then
1
Y
 is equal to:
(g= gravitational acceleration )
[2015]
A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM. If the Young's modulus of the material of the wire is Y then
1
Y
 is equal to:
(g= gravitational acceleration )
[2015]
Q.136 Correct
Q.136 In-correct
Q.136 Unattempt
A body is in simple harmonic motion with time period half second (T=0.5s) and amplitude one cm(A=1cm). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude.
[Online April 19,2014]
A body is in simple harmonic motion with time period half second (T=0.5s) and amplitude one cm(A=1cm). Find the average velocity in the interval in which it moves form equilibrium position to half of its amplitude.
[Online April 19,2014]
Q.137 Correct
Q.137 In-correct
Q.137 Unattempt
Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a,b,c are positive constants?
[Online April 12,2014]
Which of the following expressions corresponds to simple harmonic motion along a straight line, where x is the displacement and a,b,c are positive constants?
[Online April 12,2014]
Q.138 Correct
Q.138 In-correct
Q.138 Unattempt
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x=a1‌cos‌ω‌t and y=a2‌cos‌2‌ω‌t traces a curve given by:
[Online April 9, 2014]
A particle which is simultaneously subjected to two perpendicular simple harmonic motions represented by; x=a1‌cos‌ω‌t and y=a2‌cos‌2‌ω‌t traces a curve given by:
[Online April 9, 2014]
Q.139 Correct
Q.139 In-correct
Q.139 Unattempt
A particle moves with simple harmonic motion in a straight line. In first τs, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then:
[2014]
A particle moves with simple harmonic motion in a straight line. In first τs, after starting from rest it travels a distance a, and in next τ s it travels 2a, in same direction, then:
[2014]
Q.140 Correct
Q.140 In-correct
Q.140 Unattempt
In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure.

What is the value of g at the place?
[Online April 19, 2014]
In an experiment for determining the gravitational acceleration g of a place with the help of a simple pendulum, the measured time period square is plotted against the string length of the pendulum in the figure.

What is the value of g at the place?
[Online April 19, 2014]
Q.141 Correct
Q.141 In-correct
Q.141 Unattempt
The amplitude of a simple pendulum, oscillating in air with a small spherical bub, decreases from 10cm108cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3 . The time in which amplitude of this pendulum will reduce from 10cm to 5cm in carbon dioxide will be close to (In5=1.601,In2=0.693).
[Online April 9, 2014]
The amplitude of a simple pendulum, oscillating in air with a small spherical bub, decreases from 10cm108cm in 40 seconds. Assuming that Stokes law is valid, and ratio of the coefficient of viscosity of air to that of carbon dioxide is 1.3 . The time in which amplitude of this pendulum will reduce from 10cm to 5cm in carbon dioxide will be close to (In5=1.601,In2=0.693).
[Online April 9, 2014]
Q.142 Correct
Q.142 In-correct
Q.142 Unattempt
Two bodies of masses 1kg and 4kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25rad∕s, and amplitude 1.6cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g=10ms−2 )

[Online April 9, 2014]
Two bodies of masses 1kg and 4kg are connected to a vertical spring, as shown in the figure. The smaller mass executes simple harmonic motion of angular frequency 25rad∕s, and amplitude 1.6cm while the bigger mass remains stationary on the ground. The maximum force exerted by the system on the floor is (take g=10ms−2 )

[Online April 9, 2014]
Q.143 Correct
Q.143 In-correct
Q.143 Unattempt
The angular frequency of the damped oscillator is given by, ω=√(
k
m
−
r2
4m2
) where k is the spring constant, mis the mass of the oscillator and r is the damping constant.
If the ratio
r2
mk
 is 8%, the change in time period compared to the undamped oscillator is approximately as follows:
[Online April 11, 2014]
The angular frequency of the damped oscillator is given by, ω=√(
k
m
−
r2
4m2
) where k is the spring constant, mis the mass of the oscillator and r is the damping constant.
If the ratio
r2
mk
 is 8%, the change in time period compared to the undamped oscillator is approximately as follows:
[Online April 11, 2014]
Q.144 Correct
Q.144 In-correct
Q.144 Unattempt
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10 s it will decrease to α times its original magnitude, where α equals
[2013]
The amplitude of a damped oscillator decreases to 0.9 times its original magnitude in 5s. In another 10 s it will decrease to α times its original magnitude, where α equals
[2013]
Q.145 Correct
Q.145 In-correct
Q.145 Unattempt
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[2013]
An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass M. The piston and the cylinder have equal cross sectional area A. When the piston is in equilibrium, the volume of the gas is V0 and its pressure is P0. The piston is slightly displaced from the equilibrium position and released. Assuming that the system is completely isolated from its surrounding, the piston executes a simple harmonic motion with frequency
[2013]
Q.146 Correct
Q.146 In-correct
Q.146 Unattempt
A mass m=1.0kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500N∕m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan?
(Take g=10m∕s2 ).
The spring is stiff enough so that it does not get distorted during the motion.

[Online April 22, 2013]
A mass m=1.0kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500N∕m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan?
(Take g=10m∕s2 ).
The spring is stiff enough so that it does not get distorted during the motion.

[Online April 22, 2013]
Q.147 Correct
Q.147 In-correct
Q.147 Unattempt
Two simple pendulums of length 1m and 4m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to :
[Online April 9,2013]
Two simple pendulums of length 1m and 4m respectively are both given small displacement in the same direction at the same instant. They will be again in phase after the shorter pendulum has completed number of oscillations equal to :
[Online April 9,2013]
Q.148 Correct
Q.148 In-correct
Q.148 Unattempt
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density sigma at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be :
[Online April 25, 2013]
A uniform cylinder of length L and mass M having cross-sectional area A is suspended, with its length vertical, from a fixed point by a massless spring, such that it is half submerged in a liquid of density sigma at equilibrium position. When the cylinder is given a downward push and released, it starts oscillating vertically with a small amplitude. The time period T of the oscillations of the cylinder will be :
[Online April 25, 2013]
Q.149 Correct
Q.149 In-correct
Q.149 Unattempt
Bob of a simple pendulum of length l is made of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then :
[Online April 23, 2013]
Bob of a simple pendulum of length l is made of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then :
[Online April 23, 2013]
Q.150 Correct
Q.150 In-correct
Q.150 Unattempt
The displacement y(t)=A‌sin(ωt+ϕ) of a pendulum for ϕ=
2π
3
 is correctly represented by
[Online May 19, 2012]
The displacement y(t)=A‌sin(ωt+ϕ) of a pendulum for ϕ=
2π
3
 is correctly represented by
[Online May 19, 2012]
Q.151 Correct
Q.151 In-correct
Q.151 Unattempt
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs S1 and S2 of force constants k1 and k2 respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2
Statement 1: If stretched by the same amount work done on S1
Statement 2: k1<k2
[2012]
This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements.
If two springs S1 and S2 of force constants k1 and k2 respectively, are stretched by the same force, it is found that more work is done on spring S1 than on spring S2
Statement 1: If stretched by the same amount work done on S1
Statement 2: k1<k2
[2012]
Q.152 Correct
Q.152 In-correct
Q.152 Unattempt
If a simple pendulum has significant amplitude (up to a factor of 1∕e of original) only in the period between t= 0 s to t=τs, then tau may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small)
[2012]
If a simple pendulum has significant amplitude (up to a factor of 1∕e of original) only in the period between t= 0 s to t=τs, then tau may be called the average life of the pendulum. When the spherical bob of the pendulum suffers a retardation (due to viscous drag) proportional to its velocity with b as the constant of proportionality, the average life time of the pendulum in second is (assuming damping is small)
[2012]
Q.153 Correct
Q.153 In-correct
Q.153 Unattempt
A ring is suspended from a point S on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take g=π2)

[Online May 19, 2012]
A ring is suspended from a point S on its rim as shown in the figure. When displaced from equilibrium, it oscillates with time period of 1 second. The radius of the ring is (take g=π2)

[Online May 19, 2012]
Q.154 Correct
Q.154 In-correct
Q.154 Unattempt
Two particles are executing simple harmonic motion of the same amplitude A and frequency omega along the x -axis. Their mean position is separated by distance X0(X0>A). If the maximum separation between them is (X0+A), the phase difference between their motion is:
[2011]
Two particles are executing simple harmonic motion of the same amplitude A and frequency omega along the x -axis. Their mean position is separated by distance X0(X0>A). If the maximum separation between them is (X0+A), the phase difference between their motion is:
[2011]
Q.155 Correct
Q.155 In-correct
Q.155 Unattempt
A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of (
A1
A2
) is:
[2011]
A mass M, attached to a horizontal spring, executes S.H.M. with amplitude A1. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A2. The ratio of (
A1
A2
) is:
[2011]
Q.156 Correct
Q.156 In-correct
Q.156 Unattempt
A wooden cube (density of wood ' d ') of side ' l ' floats in a liquid of density ' ρ ' with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period 'T'
[2011 RS]
A wooden cube (density of wood ' d ') of side ' l ' floats in a liquid of density ' ρ ' with its upper and lower surfaces horizontal. If the cube is pushed slightly down and released, it performs simple harmonic motion of period 'T'
[2011 RS]
Q.157 Correct
Q.157 In-correct
Q.157 Unattempt
If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?
[2009]
If x,v and a denote the displacement, the velocity and the acceleration of a particle executing simple harmonic motion of time period T, then, which of the following does not change with time?
[2009]
Q.158 Correct
Q.158 In-correct
Q.158 Unattempt
A point mass oscillates along the x -axis according to the law x=x0‌cos(ωt−π∕4). If the acceleration of the particle is written as a=A‌cos(ωt+δ), then
[2007]
A point mass oscillates along the x -axis according to the law x=x0‌cos(ωt−π∕4). If the acceleration of the particle is written as a=A‌cos(ωt+δ), then
[2007]
Q.159 Correct
Q.159 In-correct
Q.159 Unattempt
A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is
[2007]
A particle of mass m executes simple harmonic motion with amplitude a and frequency v. The average kinetic energy during its motion from the position of equilibrium to the end is
[2007]
Q.160 Correct
Q.160 In-correct
Q.160 Unattempt
Two springs, of force constants k1 and k2 are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes

[2007]
Two springs, of force constants k1 and k2 are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k1 and k2 are made four times their original values, the frequency of oscillation becomes

[2007]
Q.161 Correct
Q.161 In-correct
Q.161 Unattempt
The displacement of an object attached to a spring and executing simple harmonic motion is given by x=2×10−2 cos‌π‌t metre. The time at which the maximum speed first occurs is
[2007]
The displacement of an object attached to a spring and executing simple harmonic motion is given by x=2×10−2 cos‌π‌t metre. The time at which the maximum speed first occurs is
[2007]
Q.162 Correct
Q.162 In-correct
Q.162 Unattempt
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
[2006]
A coin is placed on a horizontal platform which undergoes vertical simple harmonic motion of angular frequency ω. The amplitude of oscillation is gradually increased. The coin will leave contact with the platform for the first time
[2006]
Q.163 Correct
Q.163 In-correct
Q.163 Unattempt
The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7mm, is 4.4m∕s. The period of oscillation is
[2006]
The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7mm, is 4.4m∕s. The period of oscillation is
[2006]
Q.164 Correct
Q.164 In-correct
Q.164 Unattempt
Starting from the origin a body oscillates simple harmonically with a period of 2s. After what time will its kinetic energy be 75% of the total energy?
[2006]
Starting from the origin a body oscillates simple harmonically with a period of 2s. After what time will its kinetic energy be 75% of the total energy?
[2006]
Q.165 Correct
Q.165 In-correct
Q.165 Unattempt
The function sin2(ωt) represents
[2005]
The function sin2(ωt) represents
[2005]
Q.166 Correct
Q.166 In-correct
Q.166 Unattempt
Two simple harmonic motions are represented by the equations y1=0.1‌sin(100πt+
π
3
) and y2=0.1‌cos‌π‌t The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
[2005]
Two simple harmonic motions are represented by the equations y1=0.1‌sin(100πt+
π
3
) and y2=0.1‌cos‌π‌t The phase difference of the velocity of particle 1 with respect to the velocity of particle 2 is
[2005]
Q.167 Correct
Q.167 In-correct
Q.167 Unattempt
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
[2005]
The bob of a simple pendulum is a spherical hollow ball filled with water. A plugged hole near the bottom of the oscillating bob gets suddenly unplugged. During observation, till water is coming out, the time period of oscillation would
[2005]
Q.168 Correct
Q.168 In-correct
Q.168 Unattempt
If a simple harmonic motion is represented by
d2x
dt2
+αx=0, its time period is
[2005]
If a simple harmonic motion is represented by
d2x
dt2
+αx=0, its time period is
[2005]
Q.169 Correct
Q.169 In-correct
Q.169 Unattempt
The total energy of a particle, executing simple harmonic motion is
where x is the displacement from the mean position, hence total energy is independent of x
[2004]
The total energy of a particle, executing simple harmonic motion is
where x is the displacement from the mean position, hence total energy is independent of x
[2004]
Q.170 Correct
Q.170 In-correct
Q.170 Unattempt
The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is (
4
3
)×1000kg∕m3. Which relationship between t and t0 is true?
[2004]
The bob of a simple pendulum executes simple harmonic motion in water with a period t, while the period of oscillation of the bob is t0 in air. Neglecting frictional force of water and given that the density of the bob is (
4
3
)×1000kg∕m3. Which relationship between t and t0 is true?
[2004]
Q.171 Correct
Q.171 In-correct
Q.171 Unattempt
A particle at the end of a spring executes S.H.M with a period t1. while the corresponding period for another spring is t2. If the period of oscillation with the two springs in series is T then
[2004]
A particle at the end of a spring executes S.H.M with a period t1. while the corresponding period for another spring is t2. If the period of oscillation with the two springs in series is T then
[2004]
Q.172 Correct
Q.172 In-correct
Q.172 Unattempt
In forced oscillation of a particle the amplitude is maximum for a frequency ω1 of the force while the energy is maximum for a frequency ω2 of the force; then
[2004]
In forced oscillation of a particle the amplitude is maximum for a frequency ω1 of the force while the energy is maximum for a frequency ω2 of the force; then
[2004]
Q.173 Correct
Q.173 In-correct
Q.173 Unattempt
A particle of mass m is attached to a spring (of spring constant k ) and has a natural angular frequency ω0. An external force F(t) proportional to cos‌ω‌t(ω≠ω0) is applied to the oscillator. The displacement of the oscillator will be proportional to
[2004]
A particle of mass m is attached to a spring (of spring constant k ) and has a natural angular frequency ω0. An external force F(t) proportional to cos‌ω‌t(ω≠ω0) is applied to the oscillator. The displacement of the oscillator will be proportional to
[2004]
Q.174 Correct
Q.174 In-correct
Q.174 Unattempt
Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is
[2003]
Two particles A and B of equal masses are suspended from two massless springs of spring constants k1 and k2, respectively. If the maximum velocities, during oscillation, are equal, the ratio of amplitude of A and B is
[2003]
Q.175 Correct
Q.175 In-correct
Q.175 Unattempt
The displacement of a particle varies according to the relation x=4(cos‌π‌t+sin‌π‌t). The amplitude of the particle is
[2003]
The displacement of a particle varies according to the relation x=4(cos‌π‌t+sin‌π‌t). The amplitude of the particle is
[2003]
Q.176 Correct
Q.176 In-correct
Q.176 Unattempt
A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement x. Which of the following statements is true ?
[2003]
A body executes simple harmonic motion. The potential energy (P.E), the kinetic energy (K.E) and total energy (T.E) are measured as a function of displacement x. Which of the following statements is true ?
[2003]
Q.177 Correct
Q.177 In-correct
Q.177 Unattempt
A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes
5T
3
. Then the ratio of
m
M
 is
[2003]
A mass M is suspended from a spring of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes
5T
3
. Then the ratio of
m
M
 is
[2003]
Q.178 Correct
Q.178 In-correct
Q.178 Unattempt
The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is
[2003]
The length of a simple pendulum executing simple harmonic motion is increased by 21%. The percentage increase in the time period of the pendulum of increased length is
[2003]
Q.179 Correct
Q.179 In-correct
Q.179 Unattempt
In a simple harmonic oscillator, at the mean position
[2002]
In a simple harmonic oscillator, at the mean position
[2002]
Q.180 Correct
Q.180 In-correct
Q.180 Unattempt
If a spring has time period T, and is cut into n equal parts, then the time period of each part will be
[2002]
If a spring has time period T, and is cut into n equal parts, then the time period of each part will be
[2002]
Q.181 Correct
Q.181 In-correct
Q.181 Unattempt
A child swinging on a swing in sitting position, stands up, then the time period if the swing will
[2002]
A child swinging on a swing in sitting position, stands up, then the time period if the swing will
[2002]
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